Everyone has heard of "stainless steel." By convention, a stainless steel is an iron based alloy containing a large addition (several percent to 20 percent) of chromium. Chromium at the surface forms a thin, adherent, nearly impermeable, and self-healing layer of chromium oxide, which slows or prevents the attack of the iron base metal by oxygen or other corrosives.
But here's a trick: stick a magnet to a piece of stainless steel. Most of the time, the magnet will stick. This is "ferritic stainless steel." Every now and then, however, a part made from more highly alloyed (and thus, more expensive) stainless steel will be "austenitic stainless steel," and will be non-magnetic. Typically austenitic stainless steels will contain even more chromium and 10 or 20 percent nickel. As a result, they're expensive, but some applications require their very high properties.
If you cooled pure liquid iron, it crystallizes into delta-ferrite, which has the crystal structure shown in the first figure. ("BCC") As it cools from white-hot to dull-red, the crystals will transform to gamma-austenite, which is the second crystal illustrated ("FCC"). Cool it down from red hot to black but still very warm, it will transform again, back to ferrite, but now referred to as "alpha." This is called an allotropic transformation, and several chemical elements (like plutonium, tin, or carbon [graphite, diamond]) undergo similar reactions.
Impurities -- called alloying elements when they're added on purpose -- change the temperatures where these changes happen, and can cause both phases to coexist in a particular temperature range. Adding chromium to iron gives ferritic stainless steel; the chromium atoms substitute for the iron atoms at random. Nickel, however, is an austenite stabilizer and at additions around 10 percent will cause the iron-chromium-nickel alloy to switch to austenite at room temperature.
The austenitic steels are often used for higher temperature applications because they can withstand a hot, corrosive environment and maintain mechanical properties to somewhat higher temperatures than the ferritic grades. Both are used in large amounts in different parts of a modern, GenII light-water reactor. A GenII reactor, or even the GenIII / III+ ones under construction, will see outlet temperatures in the low-300s Celsius. The GenIV concepts will push as far as 1000°C, and the current crop of materials would turn buttery there. The austenitic alloys show better resistance to creep at high temperature than the ferritics, but under neutron bombardment they also suffer void swelling which can compromise their mechanical strength.
There's been a large amount of work on nickel base superalloys for these types of applications; Hastelloy X, as one previous commenter mentioned, being a strong contender. A nickel superalloy is "nickel-based," but even that is more of an honorary distinction: modern superalloys can contain dozens of alloying elements, with nickel being barely more than 50%. Superalloys have nearly seven decades of proven use in jet engines and land-based gas turbines. However, even these very super alloys will be hard pressed to withstand the temperatures and neutron doses and corrosive coolants in a GenIV plant. They have good potential, particularly for the regions of a GenIV plant operating short of the highest conceived temperatures, but problems such as radiation induced segregation and radiation induced precipitation of particles such as carbides at grain boundaries can be pronounced. Nickel also suffers internal helium generation during neutron irradiation, which can form small dispersed bubbles. Undoubtedly, superalloys will have a part in GenIV reactors but it remains to be seen how large or small.
The most interesting new class of materials are the F/M "ferritic-martensitic" materials and the ODS "oxide dispersion strengthened" materials. Recall that austenite is the higher-temperature phase of iron; quench austenite in water and instead of transforming to the low-temperature ferrite phase, the rushed reactor forms martensite, which is a slight variation on the ferrite structure. Martensite, however, is spectacularly hard but brittle. Mixing ferrite and martensite into a structure gives composite properties superior to either alone. The fossil energy research programs resemble nuclear in that they are always striving for longer-life components at higher temperature. Fossil energy research has yielded a number of promising F-M steels that may show good corrosion, temperature, and neutron resistance. However, like for superalloys, the database of long-term radiation-exposure data is incomplete. A variation on this theme is ODS, where F-M materials have a fine dispersion of yttrium oxide particles less than 2 nm in diameter dispersed through the structure. This high density of nanoparticles results in a large amount of matrix-particle surface area, which vacuums up radiation-induced defects such as vacancies or helium, significantly reducing the action of radiation induced segregation and precipitation. Again, long term studies are underway, but the smart money is for a mix of superalloys and ODS alloys in the GenIV prototypes.
A. F. Rowcliffe, L. K. Mansur, D. T. Hoelzer and R. K. Nanstad: Perspectives on radiation effects in nickel-base alloys for applications in advanced reactors. Journal of Nuclear Materials V392, (2009), P.341-332.
K. L. Murty and I. Charit: Structural materials for Gen-IV nuclear reactors: Challenges and opportunities. Journal of Nuclear Materials V383, (2008), P.189-195.
T. R. Allen and J. T. Busby: Radiation damage concerns for extended light water reactor service. JOM V61(7), (2009), P.29-34.
T. Allen, H. Burlet, R. K. Nanstad, M. Samaras and S. Ukai: Advanced Structural Materials and Cladding. MRS Bulletin V34(1), (2009), P.20-27.
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